Q: What are the factor combinations of the number 474,344?

 A:
Positive:   1 x 4743442 x 2371724 x 1185868 x 5929313 x 3648826 x 1824452 x 9122104 x 4561
Negative: -1 x -474344-2 x -237172-4 x -118586-8 x -59293-13 x -36488-26 x -18244-52 x -9122-104 x -4561


How do I find the factor combinations of the number 474,344?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 474,344, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 474,344
-1 -474,344

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 474,344.

Example:
1 x 474,344 = 474,344
and
-1 x -474,344 = 474,344
Notice both answers equal 474,344

With that explanation out of the way, let's continue. Next, we take the number 474,344 and divide it by 2:

474,344 ÷ 2 = 237,172

If the quotient is a whole number, then 2 and 237,172 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 237,172 474,344
-1 -2 -237,172 -474,344

Now, we try dividing 474,344 by 3:

474,344 ÷ 3 = 158,114.6667

If the quotient is a whole number, then 3 and 158,114.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 2 237,172 474,344
-1 -2 -237,172 -474,344

Let's try dividing by 4:

474,344 ÷ 4 = 118,586

If the quotient is a whole number, then 4 and 118,586 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 4 118,586 237,172 474,344
-1 -2 -4 -118,586 -237,172 474,344
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

12481326521044,5619,12218,24436,48859,293118,586237,172474,344
-1-2-4-8-13-26-52-104-4,561-9,122-18,244-36,488-59,293-118,586-237,172-474,344

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